The best way to find this equation manually is by using the least squares method. That is, we need to find the values of such that the squared vertical distance between each point and the quadratic curve is minimal.
The matrix equation for the quadratic curve is given by:
The relative predictive power of a quadratic model is denoted by .
This can be obtained using the formula:
The value of varies between and . The closer the value is to , the more accurate the model is.
But these are very tedious calculations. So, we will use a graphing calculator to automatically calculate the curve.
Consider the set of data. Determine the quadratic regression for the set.
Enter the -coordinates and -coordinates in your calculator and do a quadratic regression. The equation of the parabola that best approximates the points is
Plot the graph. You should get a graph like this.
You can see that the value for the data is .